Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 4x - 5$ and $ JT = 9x - 15$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {4x - 5} = {9x - 15}$ Solve for $x$ $ -5x = -10$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 4({2}) - 5$ $ JT = 9({2}) - 15$ $ CJ = 8 - 5$ $ JT = 18 - 15$ $ CJ = 3$ $ JT = 3$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {3} + {3}$ $ CT = 6$